This protocol is a multi center, phase I dose escalation study of SC-55494 in patients with advanced malignancy receiving cancer chemotherapy. SC-55494 is an IL-3 receptor agonist with enhanced multi lineage hematopoietic growth factor activity. The purpose of the study is to determine the safety and maximum tolerated dose of SC-55494 administered before or after chemotherapy. Secondary objectives are to obtain information on the ability of SC-55494 to limit chemotherapy-induced thrombocytopenia and neutropenia, to assess antibody production to SC-55494, and to measure SC-55494 serum levels. The study is open to previously treated or untreated patients with malignancies that may benefit from combination chemotherapy with paclitaxel and carboplatin. This combination of drugs has activity in a wide range of malignancies and is relatively well tolerated with its major toxicities being neutropenia and thrombocytopenia. The study design features staggered dosing so that the safety and tolerability of SC-55494 can be determined in a cohort of patients who receive the study drug at each dose level before chemotherapy (Group A) and before any patient receives that dose of SC-55494 after chemotherapy (Groups B and C). Group A patients will receive 7 days of drug followed by a 3 day rest period to allow for clearance of drug before receiving chemotherapy with carboplatin and paclitaxel. This group will be assessed on the GCRC to obtain the pharmacokinetic data. We have studied 3 patients on arm A on the GCRC under this protocol. Dose escalation continues. The safety and tolerability of SC-55494 will be assessed by monitoring adverse events, physical examinations, vital signs, and clinical laboratory results.